When i boot my xbox up the tv will stay blank but i will hear the sounds that it usaully makes when it logs into my account.

This Problem is well known threw out most 360 repair shops.
The G.P.U. has lost the video feed due to thermal expansion
of the P.C. board. The remedy 9/10 is to have the G.P.U
re-flowed and then securely clamp to the heat sink. This
will yield the most durable repair . Cost will very 60.00-80.00
depending on warranty and track record of the shop.

If you need more info feel free to ask.

Rob

First thing to try, disconnect the AV cable and re connect.. Or if its the type with the switch that goes from HD to TV, flip it and see if it works

If none of that works, and your box is less than three years old, call Microsoft ( 1 800 MYXBOX ) and see what they suggest.